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Continuous dependence of a coupled system of Wave-Plate Type

Year 2017, , 1389 - 1393, 01.12.2017
https://doi.org/10.16984/saufenbilder.319522

Abstract

In this study, we prove
continuous dependence of solutions on coefficients of a coupled system of
wave-plate type.

References

  • [1] K.A. Ames, L.E. Payne, “Continuous dependence results for solutions of the Navier-Stokes equations backward in time,” Nonlinear Anal. Theor. Math. Appl., 23, 103-113, 1994.
  • [2] A.O. Çelebi, V.K. Kalantarov, D. Ugurlu, “On continuous dependence on coefficients of the Brinkman-Forchheimer equations,” Appl. Math. Lett., 19, 801-807, 2006
  • [3] A.O. Çelebi, V.K. Kalantarov, D. Ugurlu, “Continuous dependence for the convective Brinkman-Forchheimer equations,” Appl. Anal. 84 (9), 877-888, 2005.
  • [4] Changhao Lin, L.E. Payne, “Continuous dependence of heatux on spatial geometry for the generalized Maxwell-Cattaneosystem,” Z. Angew. Math. Phys. 55, 575-591, 2004.
  • [5] F. Franchi, B. Straughan, “A continuous dependence on the body force for solutions to the Navier- Stokes equations and on the heat supply in a model for double-diffusive porous convection,” J. Math. Anal. Appl. 172, 117-129, 1993.
  • [6] F. Franchi, B. Straughan, “Continuous dependence on the relaxation time and modelling, and unbounded growth,”J. Math. Anal. Appl. 185, 726-746, 1994.
  • [7] F. Franchi, B. Straughan, “Spatial decay estimates and continuous dependence on modelling for an equation from dynamo theory,” Proc. R. Soc. Lond. A 445, 437-451, 1994.
  • [8] F. Franchi, B. Straughan, “Continuous dependence and decay for the Forchheimer equations,” Proc. R. Soc. Lond. Ser. A 459,3195-3202, 2003.
  • [9] Yan Li, C. Lin, “Continuous dependence for the nonhomogeneous Brinkman-Forchheimer equations in a semi-infnite pipe,” Appl. Mathematics and Computation 244, 201-208, 2014.
  • [10] C. Lin, L.E. Payne, “Continuous dependence on the Soret coefficient for double diffusive convection in Darcy ow,” J. Math. Anal. Appl. 342 , 311-325, 2008.
  • [11] Y. Liu, “Convergence and continuous dependence for the Brinkman-Forchheimer equations,” Math. Comput. Model. 49, 1401-1415, 2009.
  • [12] Y. Liu, Y. Du, C.H. Lin, “Convergence and continuous dependence results for the Brinkman equations,” Appl. Math. Comput. 215 , 4443-4455, 2010.
  • [13] L.E. Payne, J.C. Song and B. Straughan,“Continuous dependence and convergence results for Brinkman and Forchheimer models with variable viscosity,” Proc. R. Soc. Lond. A 45S , 2173-2190, 1999.
  • [14] L.E. Payne, B. Straughan, “Convergence and continuous dependence for the Brinkman-Forchheimer equations,” Stud. Appl. Math. 102, 419-439, 1999.
  • [15] M.L. Santos, J.E. Munoz Rivera, “Analytic property of a coupled system of wave-plate type with thermal effect,” Differential Integral Equations 24(9-10), 965-972, 2011.
  • [16] N.L. Scott, “Continuous dependence on boundary reaction terms in a porous medium of Darcy type,” J. Math. Anal. Appl. 399, 667-675, 2013.
  • [17] N.L. Scott, B. Straughan, “Continuous dependence on the reaction terms in porous convection with surface reactions,” Quart. Appl. Math. (in press).
  • [18] B. Straughan, “The Energy Method, Stability and Nonlinear Convection,”Appl. Math. Sci. Ser., second ed., vol. 91, Springer, 2004.
  • [19] B. Straughan, “Stability and Wave Motion in Porous Media,” Appl. Math. Sci. Ser., vol. 165, Springer, 2008.
  • [20] B. Straughan, “Continuous dependence on the heat source in resonant porous penetrative convection,” Stud. Appl. Math. 127 , 302-314, 2011.
  • [21] M. Yaman, Ş. Gür, “Continuous dependence for the pseudoparabolic equation,” Bound. Value Probl. , Art. ID 872572, 6 pp., 2010.
  • [22] M. Yaman, Ş. Gür, “Continuous dependence for the damped nonlinear hyperbolic equation,” Math. Comput. Appl. 16 (2), 437-442, 2011.
  • [23] G. Tang, Y. Liu, W. Liao, “Spatial behavior of a coupled systemof wave-plate type,” Abstract and Applied Analysisv volume 2014, Article ID 853693, 13 pages.
  • [24] H. Tu, C. Lin,” Continuous dependence for the Brinkman equations of ow in double-diffusive convection,” Electron. J. Diff. Eq. 92 , 1-9, 2007.

Wave-Plate Tipi denklem sisteminin sürekli bağımlılığı

Year 2017, , 1389 - 1393, 01.12.2017
https://doi.org/10.16984/saufenbilder.319522

Abstract

Bu çalışmada, wave-plate tipi denklem sisteminin çözümlerinin
katsayılara sürekli bağımlılığı ispatlanmıştır.

References

  • [1] K.A. Ames, L.E. Payne, “Continuous dependence results for solutions of the Navier-Stokes equations backward in time,” Nonlinear Anal. Theor. Math. Appl., 23, 103-113, 1994.
  • [2] A.O. Çelebi, V.K. Kalantarov, D. Ugurlu, “On continuous dependence on coefficients of the Brinkman-Forchheimer equations,” Appl. Math. Lett., 19, 801-807, 2006
  • [3] A.O. Çelebi, V.K. Kalantarov, D. Ugurlu, “Continuous dependence for the convective Brinkman-Forchheimer equations,” Appl. Anal. 84 (9), 877-888, 2005.
  • [4] Changhao Lin, L.E. Payne, “Continuous dependence of heatux on spatial geometry for the generalized Maxwell-Cattaneosystem,” Z. Angew. Math. Phys. 55, 575-591, 2004.
  • [5] F. Franchi, B. Straughan, “A continuous dependence on the body force for solutions to the Navier- Stokes equations and on the heat supply in a model for double-diffusive porous convection,” J. Math. Anal. Appl. 172, 117-129, 1993.
  • [6] F. Franchi, B. Straughan, “Continuous dependence on the relaxation time and modelling, and unbounded growth,”J. Math. Anal. Appl. 185, 726-746, 1994.
  • [7] F. Franchi, B. Straughan, “Spatial decay estimates and continuous dependence on modelling for an equation from dynamo theory,” Proc. R. Soc. Lond. A 445, 437-451, 1994.
  • [8] F. Franchi, B. Straughan, “Continuous dependence and decay for the Forchheimer equations,” Proc. R. Soc. Lond. Ser. A 459,3195-3202, 2003.
  • [9] Yan Li, C. Lin, “Continuous dependence for the nonhomogeneous Brinkman-Forchheimer equations in a semi-infnite pipe,” Appl. Mathematics and Computation 244, 201-208, 2014.
  • [10] C. Lin, L.E. Payne, “Continuous dependence on the Soret coefficient for double diffusive convection in Darcy ow,” J. Math. Anal. Appl. 342 , 311-325, 2008.
  • [11] Y. Liu, “Convergence and continuous dependence for the Brinkman-Forchheimer equations,” Math. Comput. Model. 49, 1401-1415, 2009.
  • [12] Y. Liu, Y. Du, C.H. Lin, “Convergence and continuous dependence results for the Brinkman equations,” Appl. Math. Comput. 215 , 4443-4455, 2010.
  • [13] L.E. Payne, J.C. Song and B. Straughan,“Continuous dependence and convergence results for Brinkman and Forchheimer models with variable viscosity,” Proc. R. Soc. Lond. A 45S , 2173-2190, 1999.
  • [14] L.E. Payne, B. Straughan, “Convergence and continuous dependence for the Brinkman-Forchheimer equations,” Stud. Appl. Math. 102, 419-439, 1999.
  • [15] M.L. Santos, J.E. Munoz Rivera, “Analytic property of a coupled system of wave-plate type with thermal effect,” Differential Integral Equations 24(9-10), 965-972, 2011.
  • [16] N.L. Scott, “Continuous dependence on boundary reaction terms in a porous medium of Darcy type,” J. Math. Anal. Appl. 399, 667-675, 2013.
  • [17] N.L. Scott, B. Straughan, “Continuous dependence on the reaction terms in porous convection with surface reactions,” Quart. Appl. Math. (in press).
  • [18] B. Straughan, “The Energy Method, Stability and Nonlinear Convection,”Appl. Math. Sci. Ser., second ed., vol. 91, Springer, 2004.
  • [19] B. Straughan, “Stability and Wave Motion in Porous Media,” Appl. Math. Sci. Ser., vol. 165, Springer, 2008.
  • [20] B. Straughan, “Continuous dependence on the heat source in resonant porous penetrative convection,” Stud. Appl. Math. 127 , 302-314, 2011.
  • [21] M. Yaman, Ş. Gür, “Continuous dependence for the pseudoparabolic equation,” Bound. Value Probl. , Art. ID 872572, 6 pp., 2010.
  • [22] M. Yaman, Ş. Gür, “Continuous dependence for the damped nonlinear hyperbolic equation,” Math. Comput. Appl. 16 (2), 437-442, 2011.
  • [23] G. Tang, Y. Liu, W. Liao, “Spatial behavior of a coupled systemof wave-plate type,” Abstract and Applied Analysisv volume 2014, Article ID 853693, 13 pages.
  • [24] H. Tu, C. Lin,” Continuous dependence for the Brinkman equations of ow in double-diffusive convection,” Electron. J. Diff. Eq. 92 , 1-9, 2007.
There are 24 citations in total.

Details

Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Yasemin Başcı

Şevket Gür This is me

Publication Date December 1, 2017
Submission Date June 7, 2017
Acceptance Date September 5, 2017
Published in Issue Year 2017

Cite

APA Başcı, Y., & Gür, Ş. (2017). Continuous dependence of a coupled system of Wave-Plate Type. Sakarya University Journal of Science, 21(6), 1389-1393. https://doi.org/10.16984/saufenbilder.319522
AMA Başcı Y, Gür Ş. Continuous dependence of a coupled system of Wave-Plate Type. SAUJS. December 2017;21(6):1389-1393. doi:10.16984/saufenbilder.319522
Chicago Başcı, Yasemin, and Şevket Gür. “Continuous Dependence of a Coupled System of Wave-Plate Type”. Sakarya University Journal of Science 21, no. 6 (December 2017): 1389-93. https://doi.org/10.16984/saufenbilder.319522.
EndNote Başcı Y, Gür Ş (December 1, 2017) Continuous dependence of a coupled system of Wave-Plate Type. Sakarya University Journal of Science 21 6 1389–1393.
IEEE Y. Başcı and Ş. Gür, “Continuous dependence of a coupled system of Wave-Plate Type”, SAUJS, vol. 21, no. 6, pp. 1389–1393, 2017, doi: 10.16984/saufenbilder.319522.
ISNAD Başcı, Yasemin - Gür, Şevket. “Continuous Dependence of a Coupled System of Wave-Plate Type”. Sakarya University Journal of Science 21/6 (December 2017), 1389-1393. https://doi.org/10.16984/saufenbilder.319522.
JAMA Başcı Y, Gür Ş. Continuous dependence of a coupled system of Wave-Plate Type. SAUJS. 2017;21:1389–1393.
MLA Başcı, Yasemin and Şevket Gür. “Continuous Dependence of a Coupled System of Wave-Plate Type”. Sakarya University Journal of Science, vol. 21, no. 6, 2017, pp. 1389-93, doi:10.16984/saufenbilder.319522.
Vancouver Başcı Y, Gür Ş. Continuous dependence of a coupled system of Wave-Plate Type. SAUJS. 2017;21(6):1389-93.

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